Give an example of a symmetric matrix $S$ in $\mathcal{S}_{2}(\mathbb{R})$ such that $\operatorname{sp}_{\mathbb{R}}(S) \subset [-1,1]$ and for which there does not exist a matrix $A \in \mathrm{O}_{2}(\mathbb{R})$ satisfying $A_{s} = S$.
Give an example of a symmetric matrix $S$ in $\mathcal{S}_{2}(\mathbb{R})$ such that $\operatorname{sp}_{\mathbb{R}}(S) \subset [-1,1]$ and for which there does not exist a matrix $A \in \mathrm{O}_{2}(\mathbb{R})$ satisfying $A_{s} = S$.